This paper presents a novel approach to image caching for image databases, web browsers, proxies and other similar applications. Current caches employ a hard strategy: either the image is stored in the cache, or it is not. In a soft cache, a variable amount of memory is assigned to each image. This is ideally matched to progressive image file formats. Our strategy for optimal soft caching considers the image download delay as a distortion measure. Then the minimization of the expected delay can be carried out in an operational rate-distortion framework. We present optimal theoretical solutions as well as simulation results.